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This has nothing to do with typed vs. untyped lambda calculus. If you want to write a type signature for emulate, it would be State⊗Integer → State⊗Integer. In general, typed lambda calculus is less expressive than untyped lambda calculus, since the latter can obviously express any well-typed expression. In this case, the typedness of the lambda calculus you're using has nothing to do with this.

No values are changing at all. He's expressing an algorithm by recursion. At cycle zero, the machine is in a known initial state. To this we apply the emulation operation which maps the old state to a new state and increments the number of cycles. If you wanted to expand this out, you'd have:

These are completely equivalent computations. In both cases, there's a serial data dependency: you can't compute the next state until you know the current state. Expressing this in lambda calculus or a purely functional style does not in any way remove this fundamental computational property. It would be like claiming that Fermat's last theorem is true in a base-12 number system but not in base-10: it's a mathematical property that's completely independent of a particular representation.

If you claim to have a faster-than-serial way to solve this emulation problem, congratulations, you've solved the halting problem and disproved one of the most fundamental theorems in computer science.

Quad, I respect you for your ability to find interesting info. I'm not sure if you're trolling or just confused, but you need to give this up.

@Qari: Real people talk about real hardware available at the time of the talk or in a reasonable period of time. You are talking about highly theoretical stuff while you apparently have no clue of real hardware.

CPUs are directly connected to the memory controller, but (a) can use HT links to access memory connected to another CPU, and (b) can respond to access requests over HT from attached IGPs and other peripherals. Normal CPU memory accesses do not go through HT.

ok i'm wrong...

simple question: can the APU(gpu) fusion access over a ht link into ram to another fusion cpu in a multisocket system ? to enable functions like Crossfire?

@Qari: Real people talk about real hardware available at the time of the talk or in a reasonable period of time. You are talking about highly theoretical stuff while you apparently have no clue of real hardware.

what if you need 'no clue' to be free to think free and without blocking limitations ?

Q, P=NP has nothing to do at all with halting problem which in term has nothing to do with P=NC.
P=NP is about whether a certain set of problems are solvable with polynomial time (might be possible to be done, who knows).
Halting problem is whether you can have a machine that can draw the conclusion that an algorithm will loop indefinitely (can't be done with a Turing machine ie any currently thinkable computer).
P=NC is the one about parallelism. Don't mix them up.

Q, P=NP has nothing to do at all with halting problem which in term has nothing to do with P=NC.
P=NP is about whether a certain set of problems are solvable with polynomial time (might be possible to be done, who knows).
Halting problem is whether you can have a machine that can draw the conclusion that an algorithm will loop indefinitely (can't be done with a Turing machine ie any currently thinkable computer).
P=NC is the one about parallelism. Don't mix them up.

the halting problem is only valid on determined systems but quantum computers are not Determinism systems...

if you build an Sedenion-dimension-quantum-computer you get an high probability of the result in one of the dimensions on the first cycle.

what if you need 'no clue' to be free to think free and without blocking limitations ?

If your premise is false, you can prove *anything*. You seem to be advocating the idea that knowing less about a subject makes you more likely to succeed in it.

Any Lynxeye's comments regarding classical vs quantum computing still stand. Nothing is added to a discussion by saying "If you build this highly theoretical computer then it might solve this problem but it might not."

If your premise is false, you can prove *anything*. You seem to be advocating the idea that knowing less about a subject makes you more likely to succeed in it.

Any Lynxeye's comments regarding classical vs quantum computing still stand. Nothing is added to a discussion by saying "If you build this highly theoretical computer then it might solve this problem but it might not."

there is one theoretical solution for the waiting for an future calculating problem.

random an number and you get a tiny chance to get the same result.

on an Sedenion based system you can have 16 dimensions of random numbers in the same time.

you only need to valid the result in the future after the calculation.

means if you calculate more than 1 problem you can get results faster by checking multiple speculativ versions in the same time and get the result faster than on an normal way.